Finite Group Databasebeta

← D3×SD16×C3⋊D3 #13176731

Subgroups — D3×SD16×C3⋊D3 #13176731

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2D3×D4×C3⋊D3C211yesmaximal, characteristic
3SD16×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×D3×SD16C211yesmaximal, characteristic, complemented
6#11723571C211yesmaximal, characteristic, complemented
7C3⋊D3×#215C211yesmaximal, characteristic, complemented
8D3×#3755C211yesmaximal, characteristic, complemented
9#11723553C211yesmaximal, characteristic, complemented
10C3⋊D3×#214C211yesmaximal, characteristic, complemented
11D3×#3754C211yesmaximal, characteristic, complemented
12#11723321C211yesmaximal, characteristic, complemented
13C3⋊D3×#204C211yesmaximal, characteristic, complemented
14D3×#3744C211yesmaximal, characteristic, complemented
15D3×C8×C3⋊D3C211yesmaximal, characteristic, complemented
16C2×SD16×C3⋊D3—31nomaximal
17D32×SD16—34nomaximal
18C22×D3×C3⋊D3—21no—
19Q8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
20D4×C3⋊(C3⋊D3)C2211yescharacteristic
21C3×Q8×C3⋊D3C2211yescharacteristic, complemented
22C3×D4×C3⋊D3C2211yescharacteristic
23C32×D3×Q8C2211yescharacteristic, complemented
24C32×D3×D4C2211yescharacteristic
25#89039—21no—
26C3⋊D3×#67—21no—
27D3×#638—21no—
28#89026C2211yescharacteristic
29C3⋊D3×D12C2211yescharacteristic
30D3×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×D3×C3⋊D3—21no—
32C4×D3×C3⋊D3C2211yescharacteristic
33#89019—21no—
34#89019C2211yescharacteristic, complemented
35C3⋊D3×Dic6—21no—
36C3⋊D3×Dic6C2211yescharacteristic, complemented
37D3×#634—21no—
38D3×#634C2211yescharacteristic, complemented
39C33×SD16C2211yescharacteristic, complemented
40#88862C2211yescharacteristic, complemented
41#88861C2211yescharacteristic, complemented
42#88851C2211yescharacteristic, complemented
43C8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
44C3×#3755C2211yescharacteristic, complemented
45C3×#3754C2211yescharacteristic, complemented
46C3×#3744C2211yescharacteristic, complemented
47C3×C8×C3⋊D3C2211yescharacteristic, complemented
48C32×#215C2211yescharacteristic, complemented
49C32×#214C2211yescharacteristic, complemented
50C32×#204C2211yescharacteristic, complemented
51C32×D3×C8C2211yescharacteristic, complemented
52#88797C2211yescharacteristic, complemented
53#88796C2211yescharacteristic, complemented
54#88795C2211yescharacteristic, complemented
55#88794C2211yescharacteristic, complemented
56#88793C2211yescharacteristic, complemented
57#88792C2211yescharacteristic, complemented
58#88785C2211yescharacteristic, complemented
59C3⋊D3×C3⋊C8C2211yescharacteristic, complemented
60D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
61C2×Q8×C3⋊D3—31no—
62C2×D4×C3⋊D3—31no—
63D32×Q8—34no—
64D32×D4—34no—
65C2×C32×SD16—31no—
66C2×#3755—31no—
67C2×#3754—31no—
68SD16×C3⋊D3—31no—
69SD16×C3⋊D3—31no—
70SD16×C3⋊D3—31no—
71SD16×C3⋊D3—31no—
72SD16×C3⋊D3—31no—
73SD16×C3⋊D3—31no—
74SD16×C3⋊D3—31no—
75SD16×C3⋊D3—34no—
76SD16×C3⋊D3—64no—
77SD16×C3⋊D3D311yescharacteristic, direct product factor
78C2×#3744—31no—
79C2×C8×C3⋊D3—31no—
80C3×D3×SD16—34no—
81C3×D3×SD16D314yescomplemented
82#63940—34no—
83D3×#215—34no—
84D3×#215—34no—
85#63930—34no—
86D3×#214—34no—
87D3×#214—34no—
88#63796—34no—
89D3×#204—34no—
90D3×#204—34no—
91D32×C8—34no—
92C22×C3⋊(C3⋊D3)—21no—
93C22×C3×C3⋊D3—21no—
94C22×C32×D3—21no—
95C2×D3×C3⋊D3—21no—
96C2×D3×C3⋊D3—21no—
97C2×D3×C3⋊D3—21no—
98C2×D3×C3⋊D3—44no—
99C2×D3×C3⋊D3D411yescharacteristic
100C33×Q8C2311yescharacteristic, complemented
101C33×D4C2311yescharacteristic
102#6312—21no—
103C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic
104C4×C3⋊(C3⋊D3)—21no—
105C4×C3⋊(C3⋊D3)C2311yescharacteristic
106#6308—21no—
107#6308C2311yescharacteristic, complemented
108C3×#638—21no—
109C3×C4⋊(C3⋊D3)C2311yescharacteristic
110C3×C4×C3⋊D3—21no—
111C3×C4×C3⋊D3C2311yescharacteristic
112C3×#634—21no—
113C3×#634C2311yescharacteristic, complemented
114C32×#67—21no—
115C32×D12C2311yescharacteristic
116C32×C4×D3—21no—
117C32×C4×D3C2311yescharacteristic
118C32×Dic6—21no—
119C32×Dic6C2311yescharacteristic, complemented
120#6293—21no—
121#6293—21no—
122#6293—21no—
123#6292—21no—
124#6291—21no—
125#6290—21no—
126#6289—21no—
127#6289D411yescharacteristic
128Dic3×C3⋊D3—21no—
129Dic3×C3⋊D3D411yescharacteristic
130D3×C3⋊Dic3—21no—
131D3×C3⋊Dic3D411yescharacteristic
132C33×C8C2311yescharacteristic, complemented
133C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic, complemented
134C3×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
135C32×C3⋊C8C2311yescharacteristic, complemented
136C2×D3×SD16—94no—
137C2×D3×SD16—91no—
138C23×C3⋊D3—61no—
139C22×D32—64no—
140C2×C32×Q8—31no—
141C2×C32×D4—31no—
142C2×#638—61no—
143Q8×C3⋊D3—31no—
144Q8×C3⋊D3—34no—
145Q8×C3⋊D3—31no—
146Q8×C3⋊D3—31no—
147Q8×C3⋊D3—61no—
148Q8×C3⋊D3—61no—
149Q8×C3⋊D3—64no—
150Q8×C3⋊D3C2×D311yescharacteristic, complemented
151D4×C3⋊D3—31no—
152D4×C3⋊D3—34no—
153D4×C3⋊D3—31no—
154D4×C3⋊D3—31no—
155D4×C3⋊D3—61no—
156D4×C3⋊D3—61no—
157D4×C3⋊D3—64no—
158D4×C3⋊D3C2×D311yescharacteristic
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4×C3⋊D3—31no—
161C2×C4×C3⋊D3—61no—
162C2×#634—31no—
163C2×#634—61no—
164C3×D3×Q8—34no—
165C3×D3×Q8C2×D314yescomplemented
166C3×D3×D4—34no—
167C3×D3×D4C2×D314yes—
168#3811—64no—
169D3×#67—64no—
170D3×#67—64no—
171#3802—34no—
172D3×D12—34no—
173D3×D12—34no—
174C4×D32—34no—
175C4×D32—64no—
176#3797—34no—
177#3797—64no—
178D3×Dic6—34no—
179D3×Dic6—34no—
180D3×Dic6—64no—
181D3×Dic6—64no—
182C32×SD16—24no—
183C32×SD16—31no—
184C32×SD16—31no—
185C32×SD16—31no—
186C32×SD16C2×D314yescomplemented
187C32×SD16C2×D311yescharacteristic, complemented
188C2×C32×C8—31no—
189#3755—31no—
190#3755—34no—
191#3755—31no—
192#3755—31no—
193#3755—64no—
194#3755C2×D311yescharacteristic, complemented
195#3754—31no—
196#3754—34no—
197#3754—31no—
198#3754—31no—
199#3754—64no—
200#3754C2×D311yescharacteristic, complemented
201C2×C3⋊(C3⋊C8)—31no—
202#3744—31no—
203#3744—31no—
204#3744—31no—
205#3744—34no—
206#3744—64no—
207#3744C2×D311yescharacteristic, complemented
208C8×C3⋊D3—31no—
209C8×C3⋊D3—31no—
210C8×C3⋊D3—34no—
211C8×C3⋊D3—31no—
212C8×C3⋊D3—64no—
213C8×C3⋊D3C2×D311yescharacteristic, complemented
214C3×#215—34no—
215C3×#215C2×D314yescomplemented
216C3×#214—34no—
217C3×#214C2×D314yescomplemented
218C3×#204—34no—
219C3×#204C2×D314yescomplemented
220C3×D3×C8—34no—
221C3×D3×C8C2×D314yescomplemented
222#3717—34no—
223#3717—34no—
224#3716—34no—
225#3716—34no—
226#3715—34no—
227#3715—34no—
228#3710—34no—
229D3×C3⋊C8—34no—
230D3×C3⋊C8—34no—
231C22×C33—21no—
232C2×C3⋊(C3⋊D3)—21no—
233C2×C3⋊(C3⋊D3)—42no—
234C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
235C2×C3×C3⋊D3—21no—
236C2×C3×C3⋊D3—42no—
237C2×C3×C3⋊D3C2×D411yescharacteristic
238C2×C32×D3—21no—
239C2×C32×D3—42no—
240C2×C32×D3C2×D411yescharacteristic
241D3×C3⋊D3—42no—
242D3×C3⋊D3—42no—
243D3×C3⋊D3—42no—
244D3×C3⋊D3SD1614yesdirect product factor
245C33×C4—21no—
246C33×C4C2411yescharacteristic
247C3⋊(C3⋊Dic3)—21no—
248C3⋊(C3⋊Dic3)C2×D411yescharacteristic
249C3×C3⋊Dic3—21no—
250C3×C3⋊Dic3C2×D411yescharacteristic
251C32×Dic3—21no—
252C32×Dic3C2×D411yescharacteristic
253C2×D3×Q8—94no—
254C2×D3×Q8—91no—
255C2×D3×D4—94no—
256C2×D3×D4—91no—
257C2×C3×SD16—34no—
258C2×C3×SD16—91no—
259C2×#215—94no—
260C2×#215—91no—
261C2×#214—94no—
262C2×#214—91no—
263D3×SD16—34no—
264D3×SD16—94no—
265D3×SD16—94no—
266D3×SD16—94no—
267D3×SD16—94no—
268D3×SD16—94no—
269D3×SD16—94no—
270D3×SD16—91no—
271D3×SD16—91no—
272D3×SD16—94no—
273D3×SD16—91no—
274D3×SD16—91no—
275D3×SD16—91no—
276D3×SD16—91no—
277D3×SD16—91no—
278D3×SD16—184no—
279D3×SD16C3⋊D311yescharacteristic, direct product factor
280C2×#204—94no—
281C2×#204—91no—
282C2×D3×C8—94no—
283C2×D3×C8—91no—
284C23×C32—61no—
285C22×C3⋊D3—21no—
286C22×C3⋊D3—31no—
287C22×C3⋊D3—61no—
288C22×C3⋊D3—61no—
289C22×C3⋊D3—61no—
290C22×C3⋊D3—61no—
291C22×C3⋊D3—64no—
292C22×C3⋊D3—124no—
293C22×C3⋊D3—124no—
294C22×C3×D3—24no—
295C22×C3×D3—64no—
296C2×D32—34no—
297C2×D32—64no—
298C2×D32—64no—
299C2×D32—64no—
300C2×D32—1216no—
301C32×Q8—24no—
302C32×Q8—31no—
303C32×Q8—61no—
304C32×Q8C22×D314yescomplemented
305C32×Q8C22×D311yescharacteristic, complemented
306C32×D4—24no—
307C32×D4—31no—
308C32×D4—61no—
309C32×D4C22×D314yes—
310C32×D4C22×D311yescharacteristic
311C2×C32×C4—31no—
312C2×C32×C4—61no—
313#638—21no—
314#638—61no—
315#638—61no—
316#638—61no—
317#638—64no—
318#638—124no—
319C2×C3⋊Dic3—31no—
320C2×C3⋊Dic3—61no—
321C4⋊(C3⋊D3)—31no—
322C4⋊(C3⋊D3)—34no—
323C4⋊(C3⋊D3)—64no—
324C4⋊(C3⋊D3)—61no—
325C4⋊(C3⋊D3)C22×D311yescharacteristic
326C4×C3⋊D3—21no—
327C4×C3⋊D3—31no—
328C4×C3⋊D3—31no—
329C4×C3⋊D3—31no—
330C4×C3⋊D3—34no—
331C4×C3⋊D3—64no—
332C4×C3⋊D3—61no—
333C4×C3⋊D3—61no—
334C4×C3⋊D3—61no—
335C4×C3⋊D3—64no—
336C4×C3⋊D3—124no—
337C4×C3⋊D3C22×D311yescharacteristic
338#634—21no—
339#634—31no—
340#634—34no—
341#634—64no—
342#634—61no—
343#634—61no—
344#634—61no—
345#634—61no—
346#634—64no—
347#634—124no—
348#634C22×D311yescharacteristic, complemented
349C3×#67—24no—
350C3×#67—64no—
351C3×D12—34no—
352C3×D12C22×D314yes—
353C3×C4×D3—24no—
354C3×C4×D3—34no—
355C3×C4×D3—64no—
356C3×C4×D3C22×D314yes—
357C3×Dic6—24no—
358C3×Dic6—34no—
359C3×Dic6—64no—
360C3×Dic6C22×D314yescomplemented
361#627—64no—
362#627—64no—
363#627—64no—
364#626—64no—
365#626—64no—
366#625—64no—
367#624—34no—
368#624—64no—
369D3×Dic3—34no—
370D3×Dic3—34no—
371D3×Dic3—64no—
372D3×Dic3—64no—
373C32×C8—24no—
374C32×C8—31no—
375C32×C8C22×D314yescomplemented
376C32×C8C22×D311yescharacteristic, complemented
377C3⋊(C3⋊C8)—31no—
378C3⋊(C3⋊C8)—34no—
379C3⋊(C3⋊C8)—64no—
380C3⋊(C3⋊C8)C22×D311yescharacteristic, complemented
381C3×C3⋊C8—34no—
382C3×C3⋊C8C22×D314yescomplemented
383C22×SD16—271noSylow
384C2×C33—41no—
385C2×C33C22×D411yescharacteristic
386C3⋊(C3⋊D3)—41no—
387C3⋊(C3⋊D3)C2×SD1612yescomplemented
388C3×C3⋊D3—41no—
389C3×C3⋊D3C2×SD1612yescomplemented
390C32×D3—41no—
391C32×D3C2×SD1612yescomplemented
392C23×D3—181no—
393C23×D3—184no—
394C2×C3×Q8—34no—
395C2×C3×Q8—91no—
396C2×C3×D4—34no—
397C2×C3×D4—91no—
398C2×#67—181no—
399C2×#67—184no—
400D3×Q8—34no—
401D3×Q8—94no—
402D3×Q8—94no—
403D3×Q8—94no—
404D3×Q8—91no—
405D3×Q8—91no—
406D3×Q8—91no—
407D3×Q8—184no—
408D3×Q8—181no—
409D3×Q8—184no—
410D3×Q8—181no—
411D3×Q8—184no—
412D3×Q8C2×C3⋊D311yescharacteristic, complemented
413D3×D4—34no—
414D3×D4—94no—
415D3×D4—94no—
416D3×D4—94no—
417D3×D4—91no—
418D3×D4—91no—
419D3×D4—91no—
420D3×D4—184no—
421D3×D4—181no—
422D3×D4—184no—
423D3×D4—184no—
424D3×D4—181no—
425D3×D4C2×C3⋊D311yescharacteristic
426C2×D12—94no—
427C2×D12—91no—
428C2×C4×D3—94no—
429C2×C4×D3—91no—
430C2×C4×D3—181no—
431C2×C4×D3—184no—
432C2×Dic6—94no—
433C2×Dic6—91no—
434C2×Dic6—181no—
435C2×Dic6—184no—
436C3×SD16—24no—
437C3×SD16—34no—
438C3×SD16—34no—
439C3×SD16—34no—
440C3×SD16—91no—
441C3×SD16—91no—
442C3×SD16—91no—
443C3×SD16D3214yescomplemented
444C3×SD16C2×C3⋊D311yescharacteristic, complemented
445C2×C3×C8—34no—
446C2×C3×C8—91no—
447#215—34no—
448#215—94no—
449#215—94no—
450#215—94no—
451#215—91no—
452#215—91no—
453#215—91no—
454#215—184no—
455#215C2×C3⋊D311yescharacteristic, complemented
456#214—34no—
457#214—94no—
458#214—94no—
459#214—94no—
460#214—91no—
461#214—91no—
462#214—91no—
463#214—184no—
464#214C2×C3⋊D311yescharacteristic, complemented
465C2×C3⋊C8—94no—
466C2×C3⋊C8—91no—
467#204—34no—
468#204—94no—
469#204—94no—
470#204—91no—
471#204—91no—
472#204—94no—
473#204—91no—
474#204—184no—
475#204C2×C3⋊D311yescharacteristic, complemented
476D3×C8—34no—
477D3×C8—94no—
478D3×C8—94no—
479D3×C8—91no—
480D3×C8—94no—
481D3×C8—91no—
482D3×C8—91no—
483D3×C8—184no—
484D3×C8C2×C3⋊D311yescharacteristic, complemented
485C22×C32—21no—
486C22×C32—24no—
487C22×C32—31no—
488C22×C32—44no—
489C22×C32—61no—
490C22×C32—122no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—31no—
493C2×C3⋊D3—34no—
494C2×C3⋊D3—34no—
495C2×C3⋊D3—42no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—61no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3—122no—
501C2×C3⋊D3—122no—
502C2×C3⋊D3—122no—
503C2×C3⋊D3—122no—
504C2×C3⋊D3—128no—
505C2×C3⋊D3—248no—
506C2×C3⋊D3D3×D411yescharacteristic
507C2×C3×D3—24no—
508C2×C3×D3—34no—
509C2×C3×D3—48no—
510C2×C3×D3—64no—
511C2×C3×D3—128no—
512C2×C3×D3D3×D414yes—
513D32—316no—
514D32—128no—
515D32—128no—
516D32—128no—
517C32×C4—21no—
518C32×C4—24no—
519C32×C4—24no—
520C32×C4—31no—
521C32×C4—44no—
522C32×C4—61no—
523C32×C4C23×D314yes—
524C32×C4C23×D311yescharacteristic
525C3⋊Dic3—21no—
526C3⋊Dic3—31no—
527C3⋊Dic3—34no—
528C3⋊Dic3—64no—
529C3⋊Dic3—61no—
530C3⋊Dic3—64no—
531C3⋊Dic3—124no—
532C3⋊Dic3D3×D411yescharacteristic
533C3×Dic3—24no—
534C3×Dic3—34no—
535C3×Dic3—64no—
536C3×Dic3D3×D414yes—
537C22×Q8—271no—
538C22×D4—271no—
539C2×SD16—31no—
540C2×SD16—91no—
541C2×SD16—271no—
542C2×SD16—271no—
543C2×SD16—271no—
544C2×SD16—271no—
545C2×SD16—271no—
546C2×SD16—271no—
547C2×SD16—271no—
548C2×SD16—271no—
549C2×SD16—271no—
550C2×SD16—271no—
551C22×C8—271no—
552C33C22×SD1611yescharacteristic, complemented, Sylow
553C23×C3—64no—
554C23×C3—181no—
555C22×D3—21no—
556C22×D3—64no—
557C22×D3—94no—
558C22×D3—91no—
559C22×D3—181no—
560C22×D3—181no—
561C22×D3—184no—
562C22×D3—184no—
563C22×D3—184no—
564C22×D3—181no—
565C22×D3—184no—
566C22×D3—181no—
567C22×D3—364no—
568C22×D3—364no—
569C22×D3—3616no—
570C3×Q8—24no—
571C3×Q8—34no—
572C3×Q8—64no—
573C3×Q8—91no—
574C3×Q8—181no—
575C3×Q8C2×D3214yescomplemented
576C3×Q8C22×C3⋊D311yescharacteristic, complemented
577C3×D4—24no—
578C3×D4—34no—
579C3×D4—64no—
580C3×D4—91no—
581C3×D4—181no—
582C3×D4C2×D3214yes—
583C3×D4C22×C3⋊D311yescharacteristic
584C2×C3×C4—34no—
585C2×C3×C4—64no—
586C2×C3×C4—91no—
587C2×C3×C4—181no—
588#67—21no—
589#67—64no—
590#67—184no—
591#67—181no—
592#67—184no—
593#67—181no—
594#67—184no—
595#67—181no—
596#67—364no—
597C2×Dic3—94no—
598C2×Dic3—91no—
599C2×Dic3—181no—
600C2×Dic3—184no—
601D12—34no—
602D12—94no—
603D12—91no—
604D12—184no—
605D12—184no—
606D12—181no—
607D12C22×C3⋊D311yescharacteristic
608C4×D3—21no—
609C4×D3—34no—
610C4×D3—64no—
611C4×D3—94no—
612C4×D3—94no—
613C4×D3—91no—
614C4×D3—94no—
615C4×D3—91no—
616C4×D3—91no—
617C4×D3—184no—
618C4×D3—181no—
619C4×D3—184no—
620C4×D3—181no—
621C4×D3—184no—
622C4×D3—184no—
623C4×D3—181no—
624C4×D3—364no—
625C4×D3C22×C3⋊D311yescharacteristic
626Dic6—21no—
627Dic6—34no—
628Dic6—64no—
629Dic6—94no—
630Dic6—91no—
631Dic6—184no—
632Dic6—181no—
633Dic6—181no—
634Dic6—184no—
635Dic6—184no—
636Dic6—184no—
637Dic6—181no—
638Dic6—184no—
639Dic6—181no—
640Dic6—364no—
641Dic6C22×C3⋊D311yescharacteristic, complemented
642C3×C8—24no—
643C3×C8—34no—
644C3×C8—91no—
645C3×C8C2×D3214yescomplemented
646C3×C8C22×C3⋊D311yescharacteristic, complemented
647C3⋊C8—34no—
648C3⋊C8—94no—
649C3⋊C8—91no—
650C3⋊C8—184no—
651C3⋊C8C22×C3⋊D311yescharacteristic, complemented
652C2×C32—24no—
653C2×C32—32no—
654C2×C32—41no—
655C2×C32—44no—
656C2×C32—84no—
657C2×C32—121no—
658C2×C32C2×D3×D414yes—
659C2×C32C2×D3×D411yescharacteristic
660C3⋊D3—32no—
661C3⋊D3—38no—
662C3⋊D3—41no—
663C3⋊D3—68no—
664C3⋊D3—121no—
665C3⋊D3—124no—
666C3⋊D3—244no—
667C3⋊D3D3×SD1612yesdirect product factor
668C3×D3—38no—
669C3×D3—44no—
670C3×D3—124no—
671C3×D3D3×SD1618yescomplemented
672C24—541no—
673C2×Q8—31no—
674C2×Q8—91no—
675C2×Q8—271no—
676C2×Q8—271no—
677C2×Q8—271no—
678C2×Q8—271no—
679C2×Q8—541no—
680C2×Q8—541no—
681C2×Q8—541no—
682C2×D4—31no—
683C2×D4—91no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—541no—
689C2×D4—541no—
690C2×D4—541no—
691C22×C4—271no—
692C22×C4—541no—
693SD16—31no—
694SD16—31no—
695SD16—31no—
696SD16—91no—
697SD16—91no—
698SD16—91no—
699SD16—271no—
700SD16—271no—
701SD16—271no—
702SD16—271no—
703SD16—271no—
704SD16—271no—
705SD16—271no—
706SD16—271no—
707SD16—271no—
708SD16D3×C3⋊D311yescharacteristic, direct product factor
709C2×C8—31no—
710C2×C8—91no—
711C2×C8—271no—
712C2×C8—271no—
713C2×C8—271no—
714C2×C8—271no—
715C22×C3—24no—
716C22×C3—21no—
717C22×C3—34no—
718C22×C3—44no—
719C22×C3—64no—
720C22×C3—91no—
721C22×C3—128no—
722C22×C3—181no—
723C22×C3—362no—
724C2×D3—21no—
725C2×D3—34no—
726C2×D3—42no—
727C2×D3—64no—
728C2×D3—916no—
729C2×D3—94no—
730C2×D3—91no—
731C2×D3—94no—
732C2×D3—128no—
733C2×D3—184no—
734C2×D3—184no—
735C2×D3—181no—
736C2×D3—364no—
737C2×D3—368no—
738C2×D3—362no—
739C2×D3—362no—
740C2×D3—368no—
741C2×D3—362no—
742C2×D3—368no—
743C2×D3—368no—
744C2×D3—362no—
745C2×D3—728no—
746C2×D3D4×C3⋊D311yescharacteristic
747C3×C4—24no—
748C3×C4—21no—
749C3×C4—24no—
750C3×C4—34no—
751C3×C4—44no—
752C3×C4—64no—
753C3×C4—91no—
754C3×C4—181no—
755C3×C4C22×D3214yes—
756C3×C4C23×C3⋊D311yescharacteristic
757Dic3—21no—
758Dic3—34no—
759Dic3—64no—
760Dic3—94no—
761Dic3—91no—
762Dic3—184no—
763Dic3—184no—
764Dic3—181no—
765Dic3—364no—
766Dic3D4×C3⋊D311yescharacteristic
767C32—24no—
768C32C2×D3×SD1614yescomplemented
769C32C2×D3×SD1611yescharacteristic, complemented
770C23—61no—
771C23—181no—
772C23—271no—
773C23—541no—
774C23—541no—
775C23—541no—
776C23—541no—
777C23—1084no—
778Q8—31no—
779Q8—61no—
780Q8—91no—
781Q8—181no—
782Q8—271no—
783Q8—541no—
784Q8—541no—
785Q8—541no—
786Q8—541no—
787Q8C2×D3×C3⋊D311yescharacteristic, complemented
788D4—31no—
789D4—61no—
790D4—91no—
791D4—181no—
792D4—271no—
793D4—541no—
794D4—541no—
795D4—541no—
796D4—541no—
797D4C2×D3×C3⋊D311yescharacteristic
798C2×C4—31no—
799C2×C4—61no—
800C2×C4—91no—
801C2×C4—181no—
802C2×C4—271no—
803C2×C4—271no—
804C2×C4—271no—
805C2×C4—271no—
806C2×C4—541no—
807C2×C4—541no—
808C2×C4—541no—
809C2×C4—541no—
810C8—31no—
811C8—91no—
812C8—271no—
813C8C2×D3×C3⋊D311yescharacteristic, complemented
814C2×C3—24no—
815C2×C3—38no—
816C2×C3—41no—
817C2×C3—44no—
818C2×C3—84no—
819C2×C3—92no—
820C2×C3—124no—
821C2×C3—361no—
822C2×C3D32×D414yes—
823C2×C3C2×D4×C3⋊D311yescharacteristic
824D3—38no—
825D3—41no—
826D3—92no—
827D3—98no—
828D3—124no—
829D3—188no—
830D3—361no—
831D3—364no—
832D3—724no—
833D3SD16×C3⋊D312yesdirect product factor
834C22—21no—
835C22—31no—
836C22—61no—
837C22—91no—
838C22—122no—
839C22—181no—
840C22—274no—
841C22—271no—
842C22—362no—
843C22—541no—
844C22—1082no—
845C22—1082no—
846C22—1082no—
847C22—1082no—
848C4—21no—
849C4—31no—
850C4—61no—
851C4—91no—
852C4—181no—
853C4—271no—
854C4—541no—
855C4C22×D3×C3⋊D311yescharacteristic
856C3—24no—
857C3D32×SD1614yescomplemented
858C3C2×SD16×C3⋊D311yescharacteristic, complemented
859C2—32no—
860C2—41no—
861C2—92no—
862C2—121no—
863C2—272no—
864C2—361no—
865C2—1081no—
866C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2D3×D4×C3⋊D3
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×SD16C22
socleC2×C33C22×D4
prime radicalD3×D4×C3⋊D3C2
hypercenterSD16D3×C3⋊D3
hypocenterC33C22×SD16
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D3×Q8×C3⋊D3C2semidirect
3. SD16×C3⋊(C3⋊D3)C2semidirect
4. C3×SD16×C3⋊D3C2semidirect
5. C32×D3×SD16C2semidirect
6. #11723571C2semidirect
7. C3⋊D3×#215C2semidirect
8. D3×#3755C2semidirect
9. #11723553C2semidirect
10. C3⋊D3×#214C2semidirect
11. D3×#3754C2semidirect
12. #11723321C2semidirect
13. C3⋊D3×#204C2semidirect
14. D3×#3744C2semidirect
15. D3×C8×C3⋊D3C2semidirect
19. Q8×C3⋊(C3⋊D3)C22semidirect
21. C3×Q8×C3⋊D3C22semidirect
23. C32×D3×Q8C22semidirect
34. #89019C22semidirect
36. C3⋊D3×Dic6C22semidirect
38. D3×#634C22semidirect
39. C33×SD16C22semidirect
40. #88862C22semidirect
41. #88861C22semidirect
42. #88851C22semidirect
43. C8×C3⋊(C3⋊D3)C22semidirect
44. C3×#3755C22semidirect
45. C3×#3754C22semidirect
46. C3×#3744C22semidirect
47. C3×C8×C3⋊D3C22semidirect
48. C32×#215C22semidirect
49. C32×#214C22semidirect
50. C32×#204C22semidirect
51. C32×D3×C8C22semidirect
52. #88797C22semidirect
53. #88796C22semidirect
54. #88795C22semidirect
55. #88794C22semidirect
56. #88793C22semidirect
57. #88792C22semidirect
58. #88785C22semidirect
59. C3⋊D3×C3⋊C8C22semidirect
60. D3×C3⋊(C3⋊C8)C22semidirect
77. SD16×C3⋊D3D3direct (N × H)
81. C3×D3×SD16D3semidirect
100. C33×Q8C23semidirect
107. #6308C23semidirect
113. C3×#634C23semidirect
119. C32×Dic6C23semidirect
132. C33×C8C23semidirect
133. C3⋊(C3⋊(C3⋊C8))C23semidirect
134. C3×C3⋊(C3⋊C8)C23semidirect
135. C32×C3⋊C8C23semidirect
150. Q8×C3⋊D3C2×D3semidirect
165. C3×D3×Q8C2×D3semidirect
186. C32×SD16C2×D3semidirect
187. C32×SD16C2×D3semidirect
194. #3755C2×D3semidirect
200. #3754C2×D3semidirect
207. #3744C2×D3semidirect
213. C8×C3⋊D3C2×D3semidirect
215. C3×#215C2×D3semidirect
217. C3×#214C2×D3semidirect
219. C3×#204C2×D3semidirect
221. C3×D3×C8C2×D3semidirect
244. D3×C3⋊D3SD16direct (N × H)
279. D3×SD16C3⋊D3direct (N × H)
304. C32×Q8C22×D3semidirect
305. C32×Q8C22×D3semidirect
348. #634C22×D3semidirect
360. C3×Dic6C22×D3semidirect
375. C32×C8C22×D3semidirect
376. C32×C8C22×D3semidirect
380. C3⋊(C3⋊C8)C22×D3semidirect
382. C3×C3⋊C8C22×D3semidirect
387. C3⋊(C3⋊D3)C2×SD16semidirect
389. C3×C3⋊D3C2×SD16semidirect
391. C32×D3C2×SD16semidirect
412. D3×Q8C2×C3⋊D3semidirect
443. C3×SD16D32semidirect
444. C3×SD16C2×C3⋊D3semidirect
455. #215C2×C3⋊D3semidirect
464. #214C2×C3⋊D3semidirect
475. #204C2×C3⋊D3semidirect
484. D3×C8C2×C3⋊D3semidirect
552. C33C22×SD16semidirect
575. C3×Q8C2×D32semidirect
576. C3×Q8C22×C3⋊D3semidirect
641. Dic6C22×C3⋊D3semidirect
645. C3×C8C2×D32semidirect
646. C3×C8C22×C3⋊D3semidirect
651. C3⋊C8C22×C3⋊D3semidirect
667. C3⋊D3D3×SD16direct (N × H)
671. C3×D3D3×SD16semidirect
708. SD16D3×C3⋊D3direct (N × H)
768. C32C2×D3×SD16semidirect
769. C32C2×D3×SD16semidirect
787. Q8C2×D3×C3⋊D3semidirect
813. C8C2×D3×C3⋊D3semidirect
833. D3SD16×C3⋊D3direct (N × H)
857. C3D32×SD16semidirect
858. C3C2×SD16×C3⋊D3semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D3×Q8×C3⋊D32
D3×D4×C3⋊D32
SD16×C3⋊(C3⋊D3)2
C3×SD16×C3⋊D32
C32×D3×SD162
#117235712
C3⋊D3×#2152
D3×#37552
#117235532
C3⋊D3×#2142
D3×#37542
#117233212
C3⋊D3×#2042
D3×#37442
D3×C8×C3⋊D32
C2×SD16×C3⋊D33
D32×SD163